Efficient Implementations of Extended Object PMBM Filters with Blocked Gibbs Sampling

TL;DR

This paper introduces efficient Gibbs sampling-based implementations for extended object PMBM filters, improving computational speed while maintaining tracking accuracy in multi-object scenarios.

Contribution

The paper develops blocked and collapsed Gibbs sampling methods for extended object PMBM filtering, enhancing efficiency over existing particle belief propagation approaches.

Findings

Achieves comparable tracking performance with significantly reduced runtime.

Blocked Gibbs sampling effectively generates high-weight hypotheses.

Collapsed Gibbs sampling improves efficiency in object initiation.

Abstract

This paper considers multiple extended object tracking based on Poisson multi-Bernoulli mixture (PMBM) filtering, which gives the closed-form Bayesian solution for standard multiple extended object models with Poisson birth. To efficiently address the challenging extended object data association problem in PMBM filtering, we develop implementations of the extended object PMBM filter using blocked Gibbs sampling. By formulating the PMBM density on an augmented state space with auxiliary variables and leveraging the Poisson object measurement model, we first derive a joint posterior over potential objects, previous global hypotheses, and current measurement association variables, together with its corresponding factorization. This factorized representation leads to blocked Gibbs samplers that efficiently generate high-weight global hypotheses and thereby provide an efficient implementation of the PMBM update step. We further introduce a collapsed Gibbs sampling variant, in which the Bernoulli object existence variables are marginalized out, yielding higher sampling efficiency, especially for the initiation of newly detected objects. The proposed methods, implemented under the gamma Gaussian inverse-Wishart model, are compared with an extended object Poisson multi-Bernoulli filter based on particle belief propagation. Simulation results demonstrate that the proposed approaches achieve comparable tracking performance while requiring substantially less runtime.